It is possible to, if you have a light source (flashlight + batteries or lantern) before interacting with the red ghost. Here's how I went about it:
-start in lab dream. be sure not to get caught by any of the banshees
-pick up the lockpick in the starting room
-use the lockpick on the door next to the starting room, and make sure to pick up all of the items within
-grab the flashlight and batteries from their rooms (first on the left banshee hallway & second on the left side of the middle hallway)
-in the left-side locker room, use the wrench on the grate, then climb through
-use the saw on the frozen body, then pick up the arm and the keycard
-go back through the grate, back around through the cafeteria, and microwave the frozen arm
-go all the way up the middle corridor with the monsters, then through the check on the right. make sure not to get caught by anything here
-go through the top door with the keycard, then use the arm on the scanner and pick up the gun
-use the gun to blast through the doors past the squidrabbit. you should still have enough stamina to get caught by it without waking up, so don't waste the ammo
-enter the elevator to go to the manor dream
-put the batteries in the flashlight if you haven't yet and turn it on. it turns off when you switch dreams.
-get the east wing key via the paint
-pray you don't get fucked by rng
-find the black dress in the various chests & put it on.
-get possessed by the red ghost, then however many of the blue ghosts you want. be mindful of your stamina here so you don't wake up too soon
-run back to of the mirror in Lady Jessica's bathroom before red ghost possession runs out
after that your character should be pregnant on waking
